A CASE STUDY ON 3D NON-LINEAR ANALYSIS OF A CLAY CORE ...

The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM)

ISSN: 2602-3199

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*Corresponding author: Ayse Bengu Sunbul-E-mail: [email protected]

© 2017 Published by ISRES Publishing: www.isres.org

The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM)

Volume 1, Pages 388-396

ICONTES2017: International Conference on Technology, Engineering and Science

A CASE STUDY ON 3D NON-LINEAR ANALYSIS OF A CLAY CORE

ROCKFILL DAM

Ayse Bengu Sunbul

Bulent Ecevit University

Murat Cavusli

Bulent Ecevit University

Murat Emre Kartal

Izmir Demokrasi University

Fatih Sunbul

Ulster University

Abstract: Clay core rockfill (CCR) dams are commonly used and the chosen model dam construction due to

their low cost and rapid construction advantages; moreover playing a key role in national water and power

management systems. In terms of large water reservoir impoundment behind a high dam, they include a risk to

the public, in case of an earthquake, especially for urban areas. Therefore, the stability of dam embankment and

analysing seismic safety is of great concern to geotechnical engineers. In fact, these analyses are complex issues

which concern both elastic and dynamic effects on the influence of the seismic response to real earthquake

records. The objective of this study is to evaluate the three dimensional static and dynamic degrading behaviour

of a CCR dam through using the finite difference method. The static part of the analysis considers the layered

construction, reservoir impoundment and vertical displacements whereas, the dynamic part considers the

response of the dam to a real earthquake recording which represents the typical measures of a peak ground

acceleration (PGA) of the study area. Dams should be designed in considering an extreme earthquake with

maximum intensity values. In view of this we have investigated the 3D non-linear seismic behaviour of a CCR

dam which was subjected to the 1999 Mw 7.1 Duzce earthquake and this is consistent with the idea of an

extreme earthquake of about maximum intensity in structural seismic response analysis. The mechanical

behavior of the dam material was described using the Mohr–Coulomb failure criterion. Dynamic analyses of the

model are performed and the dam behaviour and possible failure phenomena presented. Discussions and

comparisons between the non-linear simulation results and existing parameters are expressed.

Keywords: 3D, rockfıll dam, earthquake

Introduction Dams have become a fundamental part of a Nation’s infrastructural body and play an important and beneficial

role in the management and development of water in river basins. The use of clay-core rockfill (CCR) dam

which is constructed with the optimum use of different geotechnical materials with a permanent clay core, is a

preferred model due to its economic reasons. In terms of large water reservoir impoundment behind a high dam,

they include risks to the public, especially for urban areas (USCOLD, 1992). In order to assess these risks

realistically for both static and dynamic states, finite element (FE) technique and finite difference method (FDM)

are the available tools used in the prediction of structural behaviour.

Several researchers have conducted analysis of various types of dams using the FEM. Westergaard (1933)

proposed one of the earliest results of the effect of reservoir on the dam based on some assumptions that, water is

incompressible; dam is rigid with a vertical face. Fok and Chopra (1985) studied the seismic response of a dam

International Conference on Technology, Engineering and Science(ICONTES) October 26 - 29, 2017 Antalya/Turkey

389

by means of absorbing boundary conditions. In the review paper by Hall (1988), the importance of both static

and dynamic analyses was explained in detail. Later studies have shown the importance of 2D and 3D FEM

modelling (e.g. Özkan, Özyazicioglu ve Aksar, 2006; Siyahi and Aslan, 2008a and 2008b; Akkose and Simsek,

2010; Kartal, 2012; Ghaedi et al., 2013). Liu et al. (2016) investigated stress, deformation and settlement

analysis of a cut-off wall in a clay core rockfill dam on thick overburden. The results show that selecting plastic

concrete with a low modulus can provide high strength of the clay core of the dam and optimize the connection

between the cut-off walls which decrease the deformation. Rashidi et al. (2017) evaluated the behavior of

rockfill dams during construction and initial impoundment using numerical modeling and instrumentation data.

They also recorded 6 years displacement values and those values showed that the most of the settlement took

place in dam construction phase compared to the following 6 years period.

Stability is expressed in terms of an overall factor of safety. Progress in the area of geotechnical numerical

modelling provide us significant results in the dam physical analysis, in considering complexity such as non-

linear behavior modelling, the evolution of the pore pressure during the construction phase and seismic loading

under real earthquake data. In fact, the determination of earthquake ground motions is a key issue for the

evaluation of the seismic safety of a dam. Seismic ground motions, at a specific dam site, are usually defined in

terms of peak ground acceleration (PGA). PGA is the highest intensity of ground motions recorded by the

seismograms. Since it is not possible to predict the seismic hazard of a given region, geotechnical engineers

consider the maximum intensity in their structural seismic response models.

The paper presents a numerical study of both static and dynamic behaviour of a clay core rockfill dam. All

analyses are conducted using a 3D finite difference modelling. Results are presented first considering static

analyses including layered constructions, reservoir impoundment and predicted vertical displacements in a

selected CCR dam; then analyses are conducted within the framework of non-linearity in vertical displacements

in order on evaluate the influence of water reservoir on the seismic response of the dam.

Modellıng

The non-linear analyses which include elasto-plastic (EPNL) and direct non-linear solutions are conducted using

the finite difference program FLAC3D. FLAC 3D is a direct finite difference program include constitutive

equations, which are elucidated gradually by regular degrees of modelling that allows large strain computations,

material anisotropies and other non-linearities. For dam analysis, the Mohr-Coulomb model is applicable as a

constitutive step (FLAC3D, 2005). Other models are also implemented into the program’s flowchart by using

programming language. At every computing step in the flowchart, incremental strains are calculated in each

elementary zone and result in gradual increase of stress derived from the relevant constitutive equations. These

steps are followed by an update in zone stress and gridpoint displacements (Roth et al. 1991; Dawson et al.

2001). Seismic loading is applied at the base of the foundation layer as a velocity excitation. The Free-field

boundaries procedure in FLAC3D aims absorbing outward waves arise from the structure. FLAC3D contains an

optional form of damping, hysteretic damping, that incorporates strain-dependent damping ratio and secant

modulus functions, allowing direct comparisons between the equivalent-linear method and the fully non-linear

method (FLAC3D, 2005). We followed the same approach in our analysis.

The example model, used in the analyses, is assumed as 35 m in height. The dam has a crest length of 225 m and

a crest width of 10 m. It was considered to store 638.000 m3 of water at maximum capacity (Fig. 1).

Figure 1. Typical cross-section of the CCR dam used in the study

Numerical methods that have been commonly used to assess the dynamic behaviour of dams mainly include the

finite element or finite difference methods-based calculations. In these calculations the non-linear analysis


390

provides the analytical basis of the study which represents the real behaviour of the soil under static

(gravitational) and dynamic loadings. In this study, we have used non-linear approach which provides a more

complete insight of the behaviour of the clay core rockfill dams and finally contribute to reach the realistic

output of the dynamic analysis. The selected material parameters for the dam are shown in Table 1.

Table 1. Foundation and soil properties used in the geotechnical analyses.

Material Properties

Material Maximum

Unit

Weight

Young’s

modulus

Cohesion Internal

friction angle

Dilation

angle

Poisson’s

Ratio

Clay Core 1.59 21 MPa 50 kPa 26° 0 0.32

Rockfill 1.99 45 MPa 0 37° 8 0.28

Gravel Filter 2.15 32 MPa 0 34° 4 0.30

Sand Filter 2.14 29 MPa 0 32° 3 0.30

Rock Pieces Filter 2.16 34 MPa 0 33° 4 0.29

Foundation 2.25 10 GPa 0 42° 10 0.25

The dam with its foundation (down to 35 m) was modelled by generating brick type zones. The free-field

boundaries procedure in FLAC3D is used in order to aim absorbing outward waves arise from the dam structure.

Assuming the height of dam as h; we extend the reservoir length up to 3h which is consistent to acquire more

realistic results in the seismic response of a dam (e.g. Bayraktar et al., 2012; Kartal et al., 2017). The dam’s

body is carried out of clay, with slope inclination of 1:2.5 upstream and 1:2.0 downstream. Filter material in both

sides of the dam is carried out of rock, gravel and sand, with slope inclination of 1:0.5 (Fig. 2).

Figure 2. The dam is assumed as having asymmetric zone sections (h: downstream length, 3h: upstream length)

with clay core and foundation (See also Table 1 for material properties used in the analysis)

In fact, the two third of Turkey, being located in a 2nd degree earthquake zone according to the Ministry of

Public works and Settlement, General Directorate of disaster affairs report (AFAD, 2016). Dams should be

designed in considering an extreme earthquake with maximum intensity values. In view of this we have

investigated the 3D non-linear seismic behaviour of the CCR dam which was subjected to the 1999 Mw 7.1

Duzce earthquake and this is consistent with the idea of an extreme earthquake of about maximum intensity in

structural seismic response analysis. Therefore, we defined the construction area as a 2nd degree earthquake zone

in our scenario that, this area has the probability to produce up to 0.4 g peak ground acceleration (PGA) value.

Therefore, the example model is subjected to the 1999 Mw 7.1 Duzce Earthquake strong ground motion data

which had 0.4 g PGA value (Fig. 3).

X

Y

Z


391

Figure 3. The 1999 Mw 7.1 Duzce earthquake accelerogram

Results Analyses were conducted in three steps in order to assess the vertical displacements. These steps include static or

dynamic analyses of vertical displacements during; a) dam’s construction phase, b) full water reservoir phase

and c) seismic excitations under real earthquake data. Three observation points (three element integration points:

PA, PB and PC), for which the time history graphs of the response quantities are plotted, are marked on the mesh

as shown in Fig. 4.

Figure 4. Mesh model presented in a cross-section with three observation points

Construction Phase

The static solutions of the dam empty-reservoir system due to its gravity load are shown in Figure 5. The

software has modelled the dam’s gravity load in 1500 steps. It is obvious that the maximum predicted

displacement values are obtained at the top of the clay core (PA) with the value of 12 cm. The vertical

displacements in this phase, are constantly increasing until the 500th step during the analysis. From this point on,

the displacements have become constant. When the other two points (PB and PC) in the dam body are examined,

the predicted vertical displacement of about 4.5 cm obtained at PB while that value is about 1.5 cm at PC. In

general, it was observed that vertical displacement values at the points near the clay core were higher than those

at the other points, and vertical displacements decreased as the distance from the clay core increased.

PA PB

PC


392

Figure 5. Vertical displacements at PA, PB and PC during construction phase

Figure 6 shows the contour diagram of the vertical displacements values obtained from static analysis in

construction phase. It is observed that the maximum displacement value is 21.59 cm in the clay core of the dam.

It has been also deduced that the vertical displacement values have decreased according to the direction from

core to the outer filter layers, the value reaches down to 5 cm.

Figure 6. Contour plot of vertical displacements during construction phase

Impounding Phase

The static analyses were also carried out for impounding phase. The reservoir water with an elevation of 35

meters was included in the model using applied pressures to the surface of the reservoir bottom and dam. During

impounding, the hydrostatic force acts on the surface of the dam body. It is assumed that the hydrostatic force is

zero at the top the dam body. The direction and the magnitude of the hydrostatic forces during the impoundment

phase are shown as arrows in Fig. 7.

FLAC3D 3.00

Itasca Consulting Group, Inc.Minneapolis, MN USA

Step 1556 Model Perspective23:15:49 Wed Sep 27 2017

Center: X: 1.194e+001 Y: 1.276e+002 Z: 2.500e-001

Rotation: X: 30.000 Y: 0.000 Z: 30.000

Dist: 1.109e+003 Mag.: 1.25Ang.: 22.500

Plane Origin: X: 0.000e+000 Y: 9.825e+001 Z: 0.000e+000

Plane Orientation: Dip: 90.000 DD: 0.000

Contour of Z-Displacement Plane: on behind Magfac = 0.000e+000

-2.1597e-001 to -2.1500e-001-2.0500e-001 to -2.0000e-001-1.9000e-001 to -1.8500e-001-1.7500e-001 to -1.7000e-001-1.6000e-001 to -1.5500e-001-1.4500e-001 to -1.4000e-001-1.3000e-001 to -1.2500e-001-1.1500e-001 to -1.1000e-001-1.0000e-001 to -9.5000e-002-8.5000e-002 to -8.0000e-002-7.0000e-002 to -6.5000e-002-5.5000e-002 to -5.0000e-002

FLAC3D 3.00



Center: X: 1.194e+001 Y: 1.276e+002 Z: 2.500e-001

Rotation: X: 30.000 Y: 0.000 Z: 30.000

Dist: 1.109e+003 Mag.: 1.25Ang.: 22.500





Contour of Z displacement

Empty reservoir state

Displacements (cm)


393

Figure 7. Meshing of the dam model; the hydrostatic force is shown as vectors

Figure 8 shows the non-linear time-history graph of the vertical displacement at PA, PB and PC during full water

reservoir phase. The maximum displacement values are observed at the dam’s crest up to 18 cm. The vertical

displacements obtained at the crest are continuously increasing up to 500th step and the value become more

stable after that point. At PB and PC, vertical displacements of 11.5 cm and 6.5 cm were calculated, respectively.

According to the predicted data, the largest displacement occurred in the clay core, which is the weakest material

of the dam body. Moreover, when the empty state and the full water state of the dam are compared, it has been

observed that the vertical displacement values occurring at the crest point of the dam increase depending on the

reservoir water. Furthermore, after starting impounding stage, it was observed that the vertical displacements

were visibly increased due to the hydrostatic pressure acting on the points B and C.

The influence of the variation of the water level in the reservoir is also compared. In both cases (empty and full

water reservoir states), we obtain higher displacement variations at PA when compared to PB and PC.

Figure 8. Vertical displacements at PA, PB and PC during impounding phase

Figure 9 shows the contour diagram of vertical displacements obtained at the dam’s body during the

impoundment phase. The maximum vertical displacement occurs at dam clay core with magnitude 41 cm. In

terms of displacement values over the filter layers; we obtained displacement with magnitude 17 cm due to

hydrostatic pressure. This value is higher than those obtained in the empty reservoir phase. The results are in

good agreement with previous studies (Parish, 2007).


394

Figure 9. Contour plot of vertical displacements during the impounding phase

Dynamic Phase

Fig. 10 shows the vertical displacement time history of the dam under seismic loading for 15 sec. The maximum

displacement occurs at dam crest (PA) with magnitude 86 cm. Those values decrease down to 45 cm at PA and

PB. The peak values are observed in the strong ground motion record in the first 5 sec period. After that time

period, we observe continuous displacement values where the residual deformations are being estimated. The

higher predicted displacements are also observed at PC when compared to PB.

Figure 10. Vertical displacements at PA, PB and PC during seismic excitation phase

Fig. 11 shows the dynamic response of the dam under earthquake loading. From Fig 11, displacement responses

increase gradually from bottom to top and displacement response of dam crest are larger than those observed at

the dam foot.

FLAC3D 3.00



Center: X: 4.250e+001 Y: 1.100e+002 Z: 2.500e-001

Rotation: X: 30.000 Y: 0.000 Z: 30.000

Dist: 1.109e+003 Mag.: 1.25Ang.: 22.500


Plane Normal: X: 0.000e+000 Y: 1.000e+000 Z: 6.123e-017



FLAC3D 3.00



Center: X: 4.250e+001 Y: 1.100e+002 Z: 2.500e-001

Rotation: X: 30.000 Y: 0.000 Z: 30.000

Dist: 1.109e+003 Mag.: 1.25Ang.: 22.500


Plane Normal: X: 0.000e+000 Y: 1.000e+000 Z: 6.123e-017




Full-water reservoir state

Displacements (cm)


395

Figure 11. Contour plot of vertical displacements during seismic excitation phase

Conclusion

In order to assess static and dynamic vertical displacements on a selected CCR dam, three dimensional non-

linear analyses were carried out. The static part of the analysis considers the vertical displacement variations

following construction phase and reservoir impoundment whereas; the dynamic part considers the response of

the dam to a real earthquake recording. The results of this study are summarized as follows;

- During the construction phase (static state); the maximum displacements were observed at the top of the

clay core (crest of the dam). The predicted displacement value was 12 cm at the crest, whereas this

value was gradually decreased in consideration of lower parts of the dam body. The 3D contour

diagram also shows that the displacement value obtained in the clay core was approximately 21.5 cm.

- During the impounding phase (static state); the predicted vertical displacement value observed at the

dam crest was 18 cm and gradually increased towards to the bottom level. The 3D contour diagram for

this case shows the maximum displacement value with magnitude 41 cm at dam clay core.

- The static state analyses show a gradual increase in the magnitude of vertical displacements during an

impounding stage where the hydrostatic force acts on the surface of the dam body and causes additional

force on the clay core section.

- During the dynamic phase; the CCR dam was subjected to the ground acceleration histories obtained by

the 1999 Mw 7.1 Duzce earthquake which had 0.4 g peak acceleration value. The seismic excitation

increased the magnitude of displacements when compared to the static phases. We observe 86 cm

vertical displacement value at the crest of the dam in the first 5 sec of recording. For the rest of seismic

excitement, the residual/permanent deformations have been also observed due to the continuous seismic

loading.

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Rotation: X: 30.000 Y: 0.000 Z: 30.000

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Dist: 1.383e+003 Mag.: 1.56Ang.: 22.500





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A CASE STUDY ON 3D NON-LINEAR ANALYSIS OF A CLAY CORE ...

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